Root Raised Cosine Filter for Shaping and Matched Filtering of Digital Baseband Signals

This document presents a MATLAB implementation that demonstrates the process of using root raised cosine (RRC) filters for both pulse shaping and matched filtering of digital baseband signals. The root raised cosine filter is a widely used filter type that performs signal smoothing and spectral shaping to better match transmission channel characteristics. Through MATLAB code examples, we illustrate how to implement an RRC filter using functions like rcosdesign() or firrcos(), specifying key parameters such as roll-off factor, filter length, and sampling rate. The implementation covers both the transmitter-side pulse shaping (to limit bandwidth and minimize inter-symbol interference) and receiver-side matched filtering (to maximize SNR). We demonstrate the complete signal processing chain including filter design, signal convolution operations, and eye diagram analysis to evaluate system performance. The document provides detailed explanations of the underlying algorithm, including the mathematical formulation of the RRC filter's impulse response and its frequency domain characteristics. Through practical code examples, we show how proper filter parameter selection can improve signal quality and transmission efficiency, thereby enhancing overall communication system performance.